Finite Group Databasebeta

← #14782878

Subgroups — #14782878

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622577C211yesmaximal, characteristic
2C2×#10622715C211yesmaximal, characteristic
3#13071240C211yesmaximal, characteristic
4#13071234C211yesmaximal, characteristic
5#13070120C212yesmaximal, complemented
6#13070119C212yesmaximal, complemented
7#13070113C212yesmaximal, complemented
8#13070108C212yesmaximal, complemented
9#13068335C211yesmaximal, characteristic
10#13068333C211yesmaximal, characteristic
11C2×C11×#340C211yesmaximal, characteristic
12C23×C8×C11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66979C2211yescharacteristic
16C2×#66979C2211yescharacteristic
17C2×#66979C2211yescharacteristic
18C22×#4318C2211yescharacteristic
19#10622825—22no—
20#10622823—22no—
21#10622715—24no—
22C2×Dic11⋊C8C2212yes—
23C2×Dic11⋊C8C2212yes—
24#10622598—21no—
25#10622598—21no—
26#10622598C2212yes—
27#10622598C2212yes—
28#10622590—21no—
29#10622589—21no—
30#10622586C2212yes—
31#10622586C2212yes—
32#10622577—24no—
33C2×#66872C2212yes—
34C2×#66871C2212yes—
35C11×#340C2212yes—
36C11×#340C2212yes—
37#10622189C2211yescharacteristic
38#10622189C2211yescharacteristic
39#10622189C2211yescharacteristic
40#10622189C2211yescharacteristic
41#10622167C2212yes—
42#10622167C2212yes—
43C23×C4×C11—21no—
44C23×C4×C11—21no—
45C23×C4×C11C2311yescharacteristic
46C22×C8×C11—22no—
47C22×C8×C11—22no—
48C22×C8×C11—22no—
49C22×C8×C11C2311yescharacteristic
50C22×C8×C11C2311yescharacteristic
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4Q814yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C11×C4⋊C4C2312yes—
59C2×C22⋊Dic11—21no—
60C2×C22⋊Dic11—21no—
61C2×C22⋊Dic11D412yes—
62#66979—22no—
63#66979—22no—
64#66979—22no—
65#66979—22no—
66#66979—22no—
67#66979Q814yes—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11D411yescharacteristic
71C2×C4⋊Dic11D411yescharacteristic
72C2×C4⋊Dic11C2311yescharacteristic
73C2×C4⋊Dic11C2311yescharacteristic
74C2×C4⋊Dic11C2311yescharacteristic
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—21no—
79C2×C4×Dic11—21no—
80C2×C4×Dic11C2312yes—
81C2×#4318—22no—
82C2×#4318—22no—
83C2×#4318D414yes—
84C22×C11⋊C8C2312yes—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89Dic11⋊C8—24no—
90Dic11⋊C8—24no—
91#66872—24no—
92#66871—24no—
93#23671—111nomaximal, Sylow
94C24×C11C2×D411yescharacteristic
95C22×C4×C11—22no—
96C22×C4×C11—24no—
97C22×C4×C11—22no—
98C22×C4×C11—42no—
99C22×C4×C11—81no—
100C22×C4×C11—81no—
101C22×C4×C11—81no—
102C22×C4×C11—81no—
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D412yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
108C22×C4×C11#4112yes—
109C22×C4×C11#4112yes—
110C22×C4×C11C2411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11C2×D412yes—
116C22×Dic11C2×D412yes—
117C2×C8×C11—21no—
118C2×C8×C11—21no—
119C2×C8×C11—21no—
120C2×C8×C11—21no—
121C2×C8×C11—21no—
122C2×C8×C11—21no—
123C2×C8×C11—44no—
124C11×C4⋊C4—24no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—22no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4C2×Q814yes—
130C22⋊Dic11—24no—
131C22⋊Dic11—24no—
132C22⋊Dic11—42no—
133C4⋊Dic11—22no—
134C4⋊Dic11—22no—
135C4⋊Dic11—21no—
136C4⋊Dic11—21no—
137C4⋊Dic11—21no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—21no—
141C4⋊Dic11—82no—
142C4⋊Dic11—82no—
143C4⋊Dic11C2×Q812yes—
144C4⋊Dic11C2×Q812yes—
145Dic11⋊C4—82no—
146Dic11⋊C4—82no—
147C4×Dic11—24no—
148C4×Dic11—22no—
149C4×Dic11—22no—
150C4×Dic11—42no—
151#4318—28no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—22no—
154C2×C11⋊C8C2×D414yes—
155C2×#428—111no—
156C2×#424—111no—
157#2317—111no—
158#2316—111no—
159#2088—112no—
160#2088—112no—
161#2087—112no—
162#2086—112no—
163#1736—111no—
164#1735—111no—
165C2×#340D1111yescharacteristic
166C23×C11—21no—
167C23×C11—21no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11#12112yes—
171C23×C11C22⋊Q812yes—
172C23×C11C22⋊Q812yes—
173C23×C11C22×D411yescharacteristic
174C2×C4×C11—24no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—84no—
181C2×C4×C11—84no—
182C2×C4×C11#12112yes—
183C2×C4×C11C22⋊Q812yes—
184C2×C4×C11C22⋊Q812yes—
185C2×C4×C11#12314yes—
186C2×C4×C11#12514yes—
187C2×C4×C11#12514yes—
188C2×C4×C11C4⋊Q814yes—
189C2×C4×C11C22×D411yescharacteristic
190C2×C4×C11C22×Q811yescharacteristic
191C2×C4×C11C22×Q811yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11C2×#4111yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C8×C11—41no—
214C8×C11—41no—
215C11⋊C8—24no—
216C22×M16—111no—
217C23×C8C2×D1111yescharacteristic
218C2×#117—111no—
219C2×#117—111no—
220C2×#117—111no—
221C22×C4⋊C4C2×D1111yescharacteristic
222C22×C4⋊C4C2×D1111yescharacteristic
223#428—224no—
224C2×#107—112no—
225C2×#106—112no—
226#424—224no—
227C2×C4⋊C8—112no—
228C2×C4⋊C8—112no—
229#389—112no—
230#389—112no—
231#389—112no—
232#389—112no—
233#389—221no—
234#389—221no—
235#385—222no—
236#384—221no—
237#382—221no—
238#380—222no—
239#340—111no—
240#340—111no—
241#340—111no—
242#340—111no—
243#340—112no—
244#340—112no—
245#340C2×D1112yes—
246#340C2×D1112yes—
247C22×C11—22no—
248C22×C11—22no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—22no—
253C22×C11#39814yes—
254C22×C11C2×#12111yescharacteristic
255C22×C11C2×C22⋊Q811yescharacteristic
256C22×C11C2×C22⋊Q811yescharacteristic
257C22×C11#57611yescharacteristic
258C22×C11#57711yescharacteristic
259C22×C11#57711yescharacteristic
260C22×C11#57811yescharacteristic
261C4×C11—44no—
262C4×C11—82no—
263C4×C11#39814yes—
264C4×C11C2×#12311yescharacteristic
265C4×C11C2×#12511yescharacteristic
266C4×C11C2×#12511yescharacteristic
267C4×C11C2×C4⋊Q811yescharacteristic
268Dic11—42no—
269Dic11—42no—
270Dic11—42no—
271Dic11—42no—
272Dic11—81no—
273Dic11—81no—
274C23×C4—21no—
275C23×C4—21no—
276C23×C4C22×D1111yescharacteristic
277C2×M16—114no—
278C2×M16—222no—
279C2×M16—222no—
280C22×C8—22no—
281C22×C8—22no—
282C22×C8—22no—
283C22×C8—112no—
284C22×C8C22×D1111yescharacteristic
285C22×C8C22×D1111yescharacteristic
286#117—114no—
287#117—222no—
288#117—222no—
289#117—222no—
290#117—222no—
291#117—222no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—22no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—111no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—222no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4Dic2214yes—
308C2×C4⋊C4C22×D1112yes—
309C2×C4⋊C4C22×D1112yes—
310C2×C22⋊C4—112no—
311C2×C22⋊C4—221no—
312C2×C22⋊C4—221no—
313C2×C42—112no—
314C2×C42—221no—
315C2×C42—221no—
316#107—224no—
317#106—224no—
318C4⋊C8—224no—
319C4⋊C8—224no—
320#95—222no—
321#95—222no—
322#95—222no—
323#95—222no—
324C2×C11—24no—
325C2×C11C2×#39811yescharacteristic
326C2×C11#306211yescharacteristic
327C2×C11#306311yescharacteristic
328C2×C11#308111yescharacteristic
329C2×C11#308211yescharacteristic
330C2×C11#308311yescharacteristic
331C2×C11#308411yescharacteristic
332C24D4×D1111yescharacteristic
333C22×C4—22no—
334C22×C4—24no—
335C22×C4—22no—
336C22×C4—42no—
337C22×C4—81no—
338C22×C4—81no—
339C22×C4—81no—
340C22×C4—81no—
341C22×C4—112no—
342C22×C4—112no—
343C22×C4—221no—
344C22×C4—221no—
345C22×C4—221no—
346C22×C4—221no—
347C22×C4C2×Dic2212yes—
348C22×C4#433912yes—
349C22×C4#433912yes—
350C22×C4D4×D1111yescharacteristic
351C22×C4D4×D1112yes—
352C22×C4#434112yes—
353C22×C4Q8×D1112yes—
354C22×C4C23×D1111yescharacteristic
355M16—228no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8—21no—
359C2×C8—21no—
360C2×C8—21no—
361C2×C8—21no—
362C2×C8—44no—
363C2×C8—114no—
364C2×C8—222no—
365C2×C8—222no—
366C4⋊C4—24no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—42no—
371C4⋊C4—112no—
372C4⋊C4—112no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—221no—
376C4⋊C4—221no—
377C4⋊C4—221no—
378C4⋊C4—221no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—882no—
382C4⋊C4—882no—
383C4⋊C4—882no—
384C4⋊C4—882no—
385C4⋊C4C2×Dic2214yes—
386C22⋊C4—224no—
387C22⋊C4—224no—
388C22⋊C4—442no—
389C42—224no—
390C42—222no—
391C42—222no—
392C42—442no—
393C11#2367111yescharacteristic, complemented, Sylow
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23#6693112yes—
399C23#6693712yes—
400C23#6694912yes—
401C23C2×D4×D1111yescharacteristic
402C2×C4—24no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—84no—
409C2×C4—84no—
410C2×C4—222no—
411C2×C4—222no—
412C2×C4—222no—
413C2×C4—222no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—222no—
418C2×C4—441no—
419C2×C4—441no—
420C2×C4—441no—
421C2×C4—441no—
422C2×C4—441no—
423C2×C4—441no—
424C2×C4—441no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—441no—
428C2×C4#6692314yes—
429C2×C4#6693112yes—
430C2×C4#6693614yes—
431C2×C4#6693712yes—
432C2×C4#6694114yes—
433C2×C4#6694214yes—
434C2×C4#6694912yes—
435C2×C4C22×Dic2211yescharacteristic
436C2×C4C2×#433911yescharacteristic
437C2×C4C2×#433911yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C2×C4C2×#434111yescharacteristic
440C2×C4C2×Q8×D1111yescharacteristic
441C8—41no—
442C8—41no—
443C8—224no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22#1062227014yes—
451C22C2×#6693111yescharacteristic
452C22C2×#6693711yescharacteristic
453C22C2×#6694911yescharacteristic
454C22#1062328811yescharacteristic
455C22#1062329311yescharacteristic
456C22#1062329311yescharacteristic
457C22#1062329711yescharacteristic
458C4—44no—
459C4—82no—
460C4—442no—
461C4—442no—
462C4—442no—
463C4—442no—
464C4—881no—
465C4—881no—
466C4#1062227014yes—
467C4C2×#6692311yescharacteristic
468C4C2×#6693611yescharacteristic
469C4C2×#6694111yescharacteristic
470C4C2×#6694211yescharacteristic
471C2—24no—
472C2C2×#1062227011yescharacteristic
473C2#1307829411yescharacteristic
474C2#1307830511yescharacteristic
475C2#1307844311yescharacteristic
476C2#1307845411yescharacteristic
477C2#1307847211yescharacteristic
478C2#1307848311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#340C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#340D11
hypocenterC11#23671
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#340

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
5. #13070120C2semidirect
6. #13070119C2semidirect
7. #13070113C2semidirect
8. #13070108C2semidirect
393. C11#23671semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106225772
C2×#106227152
#130712402
#130712342
#130701202
#130701192
#130701132
#130701082
#130683352
#130683332
C2×C11×#3402
#2367111